There were 307 gold, yellow and red markers in a box. 7 red markers were removed from the box and the ratio of the number of gold markers to the number of yellow markers to the number of red markers became 4 : 2 : 9. Then some grey markers were added and the ratio of the number of red markers to the number of grey markers was 9 : 8.
- What was the ratio of the number of gold markers to the number of yellow markers to the number of red markers at first?
- How many markers were in the box in the end?
|
Gold |
Yellow |
Red |
Grey |
Total |
Before |
4 u |
2 u |
9 u + 7 |
0 |
307 |
Change 1 |
No change |
No change |
- 7 |
|
- 7 |
After 1 |
4 u |
2 u |
9 u |
|
300 |
Change 2 |
No change |
No change |
No change |
+ 8 u |
|
After 2 |
4 u |
2 u |
9 u |
8 u |
|
(a)
Total number of markers at first
= 4 u + 2 u + 9 u + 7
= 15 u + 7
15 u + 7 = 307
15 u = 307 - 7
15 u = 300
1 u = 300 ÷ 15 = 20
Number of gold markers at first
= 4 u
= 4 x 20
= 80
Number of yellow markers at first
= 2 u
= 2 x 20
= 40
Number of red markers at first
= 9 u + 7
= 9 x 20 + 7
= 187
At first
Gold markers : Yellow markers : Red markers
80 : 40 : 187
(b)
Total number of markers in the box in the end
= 4 u + 2 u + 9 u + 8 u
= 23 u
= 460
Answer(s): (a) 80 : 40 : 187; (b) 460